The Gromov Invariants of Ruan-Tian and Taubes

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dc.creatorIonel, Eleny-Nicoleta
dc.creatorParker, Thomas H.
dc.date1997-02-06
dc.date.accessioned2026-07-07T09:07:11Z
dc.date.available2026-07-07T09:07:11Z
dc.descriptionTaubes has recently defined Gromov invariants for symplectic four-manifolds and related them to the Seiberg-Witten invariants. Independently, Ruan and Tian defined symplectic invariants based on ideas of Witten. In this note, we show that Taubes' Gromov invariants are equal to certain combinations of Ruan-Tian invariants. This link allows us to generalize Taubes' invariants. For each closed symplectic four-manifold, we define a sequence of symplectic invariants $Gr_δ$, $δ=0,1,2,...$. The first of these, $Gr_0$, generates Taubes' invariants, which count embedded J-holomorphic curves. The new invariants $Gr_δ$ count immersed curves with $δ$ double points. In particular, these results give an independent proof that Taubes' invariants are well-defined. They also show that some of the Ruan-Tian symplectic invariants agree with the Seiberg-Witten invariants.
dc.descriptionAMS-LaTeX, 11 pages
dc.identifierhttps://arxiv.org/abs/alg-geom/9702008
dc.identifierhttp://arxiv.org/abs/alg-geom/9702008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150278
dc.subjectAlgebraic Geometry
dc.titleThe Gromov Invariants of Ruan-Tian and Taubes
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